You are asked to find the height of a light pole that needs to be replaced at the local high school football field.

Question

The problem is that the pole is so old that there is no record of its height. Describe a way that you could figure out the height of the pole with out measuring it directly. (you do not have access to a crane or a lift that will allow you to drop a measuring tape from the top. You need to come up with a way to measure the height without actually measuring the pole itself).

Answer 1

Use similar right triangles.

 

 

On a sunny day, measure the length of the shadow cast on the ground by the pole. Know the height of the person, and measure his/her shadow cast on the ground at the same time as the pole shadow measurement.

 

 

Using proportions.     shadow of person: shadow of pole = height of person: unknown height of pole.

Using the cross product property of proportions will yield the height of the pole.

 

Example:

 

8 ft shadow: 28 ft shadow = 6 ft person: X ft high pole

 

8X = 28•6

 

8X = 168

 

X = 21 ft high pole